Two wires of same material having lengths and radius in the ratio of \(3: 4\) and \(3: 2\) respectively are connected in parallel with a potential source of 6 V . The ratio of currents flowing through them \(I_1: I_2=\) ________.

A \(1: 3\)
B \(3: 1\)
C \(1: 2\)
D \(2: 1\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(3: 1\)

Step-by-step Solution

Detailed explanation

(B)
Both wires are connected in parallel.
\(I_1 R_1=I_2 R_2\)
\(\therefore \frac{ I _1}{ I _2}=\frac{ R _2}{ R _1}=\frac{\rho \frac{l_2}{\pi r_2^2}}{\rho \frac{l_1}{\pi r_1^2}}\)
\(\therefore \frac{ I _1}{ I _2}=\frac{l_2}{l_1} \times\left(\frac{r_1}{r_2}\right)^2\)
\(\begin{array}{l}\therefore \frac{I_1}{I_2}=\frac{4}{3} \times\left(\frac{3}{2}\right)^2 \\ \therefore \frac{I_1}{I_2}=\frac{3}{1}\end{array}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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